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Attempt to prove Euclid 's fifth postula...

Attempt to prove Euclid 's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

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All attempts to prove the fifth postulate as a theorem led to a great achievement in the creation of several other geometries. These geometries are quite different from Euclidean geometry and called non - Euclidean geometry.
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Consider two ‘postulates’ given below: (i) Given any two distinct points A and B, there exists a third point C which is in between A and B. (ii) There exist at least three points that are not on the same line. Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.

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NCERT EXEMPLAR-INTRODUCTION TO EUCLID GEOMETRY-Introduction To Euclid Geometry
  1. "For every line L and for every point P not lying on a given line L, t...

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  2. Two distinct intersecting lines cannot be parallel to the same line.

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  3. Attempt to prove Euclid 's fifth postulate using the other postulates ...

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  4. Two salesmen make equal sales during the month of August. In September...

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  5. It is known that x+y=10 and that x=z. Show that z+y=10.

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  6. Look at the adjoining figure. Show that length AH gt sum of lengths of...

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  7. In the adjoining figure, if AB = BC and BX =BY, then show that AX=CY

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  8. In the adjoining figure , we have X and Y are the mid - point of A...

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  9. In the adjoining figure , if BX=(1)/(2)AB,BY=(1)/(2)BCand AB=BC, then...

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  10. In the adjoining figure, we have angle1=angle2 and angle 2 =angle3. S...

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  11. In the adjoining figure, we have angle1=angle3 and angle2=angle4. Sho...

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  12. In the ajoining figure , we haveangleABC=angleACBand angle3=angle4. Sh...

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  13. In the adjoining figure , we have AC=DC and CB = CE. Show that AB=DE.

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  14. In the adjoining figure, OX =1/2XY, PX =1/2XZ and OX =PX. Show that XY...

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  15. In the adjoining figure (i) AB=BC, M is the mid -point of A...

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  16. Read the following statements: An equilateral triangle is a polygon ...

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  17. Study the following statements " Two intersecting lines cannot ...

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  18. Read the following statements which are taken as axioms (i) If a t...

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  19. Read the following two statements which are taken as axiom: (i) If ...

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  20. Read the following axioms (i) Things which are equal to the same th...

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